Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data

2015/07/30 by Maria Colombo, Colombo, Maria, Federico Stra +1
Mathematics · Physics and Astronomy · #35Q40 #49Q20 #49S05 #81Q05 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35Q40 #msc:49Q20 #msc:49S05 #msc:81Q05

paper · pdf · doi:10.48550/arxiv.1507.08522

21 pages, 5 figures

arxiv created 2015/07/30 · openalex publication_date 2015/07/30 · arxiv updated 2015/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We disprove a conjecture in Density Functional Theory, relative to multimarginal optimal transport maps with Coulomb cost. We also provide examples of maps satisfying optimality conditions for special classes of data.

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